CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 210
Author(s):  
Vladimir Ch. Zhukovsky
Keyword(s):  
Domain Walls ◽  
Analytic Solutions ◽  
Space Time ◽  
Monolayer Graphene ◽  
Dirac Fermion ◽  
Induced Current ◽  
Bohm Potential ◽  
Exact Analytic Solutions ◽  
Compact Dimension ◽  
Aharonov Bohm

We consider fermion models in 3D- and 5D-space-time with an Aharonov–Bohm potential and a domain wall. Induced current is calculated, which is due to vacuum effects in the topologically nontrivial space-time. Violation of chiral symmetry and appearance of induced current is demonstrated in a simple example of quantum mechanical violation of symmetry in a model of a massless Dirac fermion moving in a background vector field and domain walls as barriers for the electron propagation. The effective Dirac equation for massless electrons modeling monolayer graphene is used. One of the solutions to the problem of describing domain walls in planar systems is reduced to finding exact analytic solutions. In this paper, we consider appearance of induced current in two-fermion model with a compact dimension as a result of vacuum polarization in the field of the external gauge field in the 4 + 1 and the 2 + 1 dimensional models with one type of fermions and with two types of fermions living in the brane and in the bulk. Two different approaches (Kaluza–Klein and Aharonov–Bohm) to the problem of induced current are used. Production of an induced current in a planar model with a thin solenoid is also studied.

scholarly journals An Archimedes' Screw for Light

2021 ◽  
Author(s):  
Emanuele Galiffi ◽  
Paloma Huidobro ◽  
John Pendry
Keyword(s):  
Analytic Solutions ◽  
Space Time ◽  
Time Varying ◽  
Pump Probe ◽  
Circularly Polarized ◽  
Polarized Beams ◽  
Exact Analytic Solutions ◽  
Potential Applications ◽  
Chiral Systems ◽  
Wide Family

Abstract An Archimedes' Screw captures water, feeding energy into it by lifting it to a higher level. We introduce the first instance of an optical Archimedes' Screw, and demonstrate how this system is capable of capturing light, dragging it and amplifying it. We unveil new exact analytic solutions to Maxwell's Equations for a wide family of chiral space-time media, and show their potential to achieve chirally selective amplification within widely tunable parity-time-broken phases. Our work, which may be readily implemented via pump-probe experiments with circularly polarized beams, opens a new direction in the physics of time-varying media by merging the rising field of space-time metamaterials and that of chiral systems, and offers a new playground for topological and non-Hermitian photonics, with potential applications to chiral spectroscopy and sensing.

scholarly journals Polarized Baryon Production in Heavy Ion Collisions: An Analytic Hydrodynamical Study

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 101 ◽  
Author(s):  
Bálint Boldizsár ◽  
Márton I. Nagy ◽  
Máté Csanád
Keyword(s):  
Perfect Fluid ◽  
Time Evolution ◽  
Heavy Ion Collisions ◽  
Degrees Of Freedom ◽  
Heavy Ion ◽  
Analytic Solutions ◽  
Baryon Production ◽  
Thermodynamical Equilibrium ◽  
Ion Collisions ◽  
Exact Analytic Solutions

In this paper, we utilize known exact analytic solutions of perfect fluid hydrodynamics to analytically calculate the polarization of baryons produced in heavy-ion collisions. Assuming local thermodynamical equilibrium also for spin degrees of freedom, baryons get a net polarization at their formation (freeze-out). This polarization depends on the time evolution of the Quark-Gluon Plasma (QGP), which can be described as an almost perfect fluid. By using exact analytic solutions, we can thus analyze the necessity of rotation (and vorticity) for non-zero net polarization. In this paper, we give the first analytical calculations for the polarization four-vector. We use two hydrodynamical solutions; one is the spherically symmetric Hubble flow (a somewhat oversimplified model, to demonstrate the methodology); and the other solution is a somewhat more involved one that corresponds to a rotating and accelerating expansion, and is thus well-suited for the investigation of some of the main features of the time evolution of the QGP created in peripheral heavy-ion collisions (although there are still numerous features of real collision geometry that are beyond the scope of this simple model). Finally, we illustrate and discuss our results on the polarization.

Study of some rheological models with a finite number of degrees of freedom

2000 ◽  
Vol 19 (2) ◽  
pp. 277-307 ◽  
Author(s):  
Jérôme Bastien ◽  
Michelle Schatzman ◽  
Claude-Henri Lamarque
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Rheological Models

scholarly journals BLACK HOLE EVAPORATION BASED UPON A q-DEFORMATION DESCRIPTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6039-6049 ◽  
Author(s):  
XIN ZHANG
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Radiation Spectrum ◽  
Correlation Effect ◽  
Space Time ◽  
Noncommutative Space ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Starting Point ◽  
New Distribution

A toy model based upon the q-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the space–time noncommutativity in the vicinity of black hole horizon. We use a trick that all the space–time noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative space–time, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cutoff of the spectrum is the prediction of the model.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Full Control of Virtual Objects Manipulation Based on the Images of Real Ones

2011 ◽  
Vol 10 (3) ◽  
pp. 51-60
Author(s):  
Brahim Nini
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Moving Object ◽  
Real Object ◽  
Virtual Object ◽  
Analytical Geometry ◽  
Six Degrees Of Freedom ◽  
Virtual Objects ◽  
Simulation Process ◽  
Full Control

This work deals with the virtual manipulation of a real object through its images. The results presented in this paper give a movie-based solution to the simulation process. We show how the simulation of infinite virtual views of a moving object can be reached using a finite number of object's taken images stored in an organized way. The basis of this solution is an analytical geometry-based method that links explicit applied user's actions, resulting in an object's views change, and images that match the best such views. This paper presents an overall solution for these three intertwined parts of the virtual manipulation that involves six degrees of freedom. Hence, a user is able to freely manipulate a virtual object in a scene in whatever manner s/he likes. In this case, the actions are transformed into rotations and/or translations which lead to some changes in object's appearance, both covered by two viewing features: zoom and/or rotations

scholarly journals Exact analytical solutions of continuously graded models of flat lenses based on transformation optics

2017 ◽  
Vol 30 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Mariana Dalarsson ◽  
Raj Mittra
Keyword(s):  
Magnetic Fields ◽  
Longitudinal Direction ◽  
Middle Layer ◽  
Analytic Solutions ◽  
Transformation Optics ◽  
Confluent Hypergeometric Functions ◽  
Graded Index ◽  
Exact Analytic Solutions ◽  
Electric And Magnetic Fields ◽  
Physical Insight

We present a study of exact analytic solutions for electric and magnetic fields in continuously graded flat lenses designed utilizing transformation optics. The lenses typically consist of a number of layers of graded index dielectrics in both the radial and longitudinal directions, where the central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while other layers act as matching layers and reduce the reflections at the interfaces of the middle layer. Such lenses can be modeled as compact composites with continuous permittivity (and if needed) permeability functions which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the proposed procedures by obtaining the exact analytic solutions for the electric and magnetic fields for one simple special class of composite designs with radially graded parameters. To this purpose we utilize the equivalence between the Helmholtz equation of our graded flat lens and the quantum-mechanical radial Schr?dinger equation with Coulomb potential, furnishing the results in the form of Kummer confluent hypergeometric functions. Our approach allows for a better physical insight into the operation of our transformation optics-based graded lenses and opens a path toward novel designs and approaches.

scholarly journals New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 374-384
Author(s):  
Mustafa Inc ◽  
E. A. Az-Zo’bi ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Muhammad Nasir Ali ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Solution Process ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Bright Solitons ◽  
Exact Analytic Solutions ◽  
Higher Dimensional ◽  
Non Local ◽  
Free Parameters ◽  
Ito Equation

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

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